On approximating complex quadratic optimization problems via semidefinite programming relaxations
نویسندگان
چکیده
منابع مشابه
On Approximating Complex Quadratic Optimization Problems via Semidefinite Programming Relaxations
In this paperwe study semidefinite programming (SDP)models for a class of discrete and continuous quadratic optimization problems in the complex Hermitian form. These problems capture a class of well-known combinatorial optimization problems, as well as problems in control theory. For instance, they include theMAX-3-CUT problem where the Laplacian matrix is positive semidefinite (in particular,...
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Given an arbitrary matrix A in which all of the diagonal elements are zero, we would like to find x1, x2, . . . , xn ∈ {−1, 1} such that ∑n i=1 ∑n j=1 aijxixj is maximized. This problem has an important application in correlation clustering, and is also related to the well-known inequality of Grothendieck in functional analysis. While solving quadratic programs is NP-hard, we can approximate th...
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In this paper we study the approximation algorithms for a class of discrete quadratic optimization problems in the Hermitian complex form. A special case of the problem that we study corresponds to the max-3-cut model used in a recent paper of Goemans and Williamson. We first develop a closed-form formula to compute the probability of a complex-valued normally distributed bivariate random vecto...
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In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and global minimum using a sequence of semidefinite programming (SDP) relaxations and provide convergence results for the methods. Our scheme for problems with a ...
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A polynomial optimization problem whose objective function is represented as a sum of positive and even powers of polynomials, called a polynomial least squares problem, is considered. Methods to transform a polynomial least squares problem to polynomial semidefinite programs to reduce degrees of the polynomials are discussed. Computational efficiency of solving the original polynomial least sq...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2006
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-006-0064-6